The minimum dissipative rate (MDR) method for deriving a coronal non-force-free
magnetic field solution is partially evaluated. These magnetic field solutions
employ a combination of three linear (constant α force-free-field solutions with
one being a potential field (i.e., α 0). We examine the particular case of the
solutions where the other two α s are of equal magnitude but of opposite signs.
This is motivated by studying the SOLIS vector magnetograms of AR 10987 which show
a global α value consistent with an α 0 value as evaluated by (Curl B)z/Bz
over the region.
Typical of the current state of the observing technology, there is no definitive twist
for input into the general MDR method. This suggests that the special α case, of two α s
with equal magnitudes and opposite signs, is appropriate given the data. Only for an
extensively twisted active region does a dominant, non-zero α normally emerge from a
distribution of local values. For a special set of conditions, we find: (i)
The resulting magnetic field is a vertically inflated magnetic field resulting from
the electric currents being parallel to the photosphere, similar to the results of
Gary and Alexander (1999). (ii) For α ~ α _max/2), the Lorentz force per unit volume
normalized by the square of the magnetic field is on the order of 1.4x10-10 cm^-1.
The Lorentz force (L_F) is a factor of ten higher than that of the magnetic
force d(B^2/8pi)/dz, a component of L_F. The calculated photospheric electric current
densities are an order smaller than the maximum observed in all active regions.
Hence both the Lorentz force density and the generated electric current density
seem to be physically consistent with possible solar dynamics. The results imply
that the field could be inflated with an over pressure along the neutral line.
(iii) However, the implementation of this or any other extrapolation method
using the electric current density as a lower boundary condition must be done
cautiously, with the current magnetography.